This rule exists to ensure that the majority of the verifiers who are verifying the blockchain cannot be excluded by attackers who are trying to take control of the blockchain. In order to control the direction of the chain, one must control more than 50% of the current active verifiers. The blocks in this and the previous two cycles are considered to avoid divergence at opportunistic moments for verifiers that are clustered around certain parts of the chain.
The metric calculated in this rule cannot increase from one block to the next unless the cycle length also increases from one block to the next. This is important because it ensures that every block that passes this rule can be extended indefinitely.
These are the only two blockchain rules, and together they guarantee that, starting at any point in the blockchain, one must control more than half of the active verifiers to continue to produce a valid version of the blockchain. Unlike proof of work, which can be manipulated at will by anyone in possession of sufficient computational resources, proof of diversity requires active participation in a particular blockchain to have any influence on that blockchain.